As shown in [1]}, denoting norming constant \(c_n=b_n/a^{\prime }(\eta _n)\) .
Then we have residue condition as follows
\(&\underset{z=\eta _n}{\rm Res} \left[\frac{\mu _{+,1}(z)}{a(z)}\right]=c_n e^{-2i\lambda (\eta _n)x}\mu _{-,2}(\eta _n),\\&\underset{z=\bar{\eta }_n}{\rm Res} \left[\frac{\mu _{+,2}(z)}{\overline{a(\bar{z})}}\right]=\bar{c}_n e^{2i\lambda (\bar{\eta }_n)x}\mu _{-,1}(\bar{\eta }_n).\) 
